Turbulence

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.^[1]

Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.^[2]^[3]^: 2 Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This increases the energy needed to pump fluid through a pipe.

The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Richard Feynman described turbulence as the most important unsolved problem in classical physics.^[4]

The turbulence intensity affects many fields, for examples fish ecology,^[5] air pollution,^[6] precipitation,^[7] and climate change.^[8]

^ Batchelor, G. (2000). Introduction to Fluid Mechanics.
^ Ting, F. C. K.; Kirby, J. T. (1996). "Dynamics of surf-zone turbulence in a spilling breaker". Coastal Engineering. 27 (3–4): 131–160. Bibcode:1996CoasE..27..131T. doi:10.1016/0378-3839(95)00037-2.
^ Tennekes, H.; Lumley, J. L. (1972). A First Course in Turbulence. MIT Press. ISBN 9780262200196.
^ Eames, I.; Flor, J. B. (17 January 2011). "New developments in understanding interfacial processes in turbulent flows". Philosophical Transactions of the Royal Society A. 369 (1937): 702–705. Bibcode:2011RSPTA.369..702E. doi:10.1098/rsta.2010.0332. PMID 21242127.
^ MacKENZIE, Brian R (August 2000). "Turbulence, larval fish ecology and fisheries recruitment: a review of field studies". Oceanologica Acta. 23 (4): 357–375. Bibcode:2000AcOc...23..357M. doi:10.1016/s0399-1784(00)00142-0. ISSN 0399-1784. S2CID 83538414.
^ Wei, Wei; Zhang, Hongsheng; Cai, Xuhui; Song, Yu; Bian, Yuxuan; Xiao, Kaitao; Zhang, He (February 2020). "Influence of Intermittent Turbulence on Air Pollution and Its Dispersion in Winter 2016/2017 over Beijing, China". Journal of Meteorological Research. 34 (1): 176–188. Bibcode:2020JMetR..34..176W. doi:10.1007/s13351-020-9128-4. ISSN 2095-6037.
^ Benmoshe, N.; Pinsky, M.; Pokrovsky, A.; Khain, A. (27 March 2012). "Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2-D simulations by a spectral mixed-phase microphysics cloud model". Journal of Geophysical Research: Atmospheres. 117 (D6): n/a. Bibcode:2012JGRD..117.6220B. doi:10.1029/2011jd016603. ISSN 0148-0227.
^ Sneppen, Albert (5 May 2022). "The power spectrum of climate change". The European Physical Journal Plus. 137 (5): 555. arXiv:2205.07908. Bibcode:2022EPJP..137..555S. doi:10.1140/epjp/s13360-022-02773-w. ISSN 2190-5444. S2CID 248652864.

[Batchelor-1] Batchelor, G. (2000). Introduction to Fluid Mechanics.

[ting-surf-2] Ting, F. C. K.; Kirby, J. T. (1996). "Dynamics of surf-zone turbulence in a spilling breaker". Coastal Engineering. 27 (3–4): 131–160. Bibcode:1996CoasE..27..131T. doi:10.1016/0378-3839(95)00037-2.

[tennekes-3] Tennekes, H.; Lumley, J. L. (1972). A First Course in Turbulence. MIT Press. ISBN 9780262200196.

[eames-quoting-feynman-4] Eames, I.; Flor, J. B. (17 January 2011). "New developments in understanding interfacial processes in turbulent flows". Philosophical Transactions of the Royal Society A. 369 (1937): 702–705. Bibcode:2011RSPTA.369..702E. doi:10.1098/rsta.2010.0332. PMID 21242127.

[5] MacKENZIE, Brian R (August 2000). "Turbulence, larval fish ecology and fisheries recruitment: a review of field studies". Oceanologica Acta. 23 (4): 357–375. Bibcode:2000AcOc...23..357M. doi:10.1016/s0399-1784(00)00142-0. ISSN 0399-1784. S2CID 83538414.

[6] Wei, Wei; Zhang, Hongsheng; Cai, Xuhui; Song, Yu; Bian, Yuxuan; Xiao, Kaitao; Zhang, He (February 2020). "Influence of Intermittent Turbulence on Air Pollution and Its Dispersion in Winter 2016/2017 over Beijing, China". Journal of Meteorological Research. 34 (1): 176–188. Bibcode:2020JMetR..34..176W. doi:10.1007/s13351-020-9128-4. ISSN 2095-6037.

[7] Benmoshe, N.; Pinsky, M.; Pokrovsky, A.; Khain, A. (27 March 2012). "Turbulent effects on the microphysics and initiation of warm rain in deep convective clouds: 2-D simulations by a spectral mixed-phase microphysics cloud model". Journal of Geophysical Research: Atmospheres. 117 (D6): n/a. Bibcode:2012JGRD..117.6220B. doi:10.1029/2011jd016603. ISSN 0148-0227.

[8] Sneppen, Albert (5 May 2022). "The power spectrum of climate change". The European Physical Journal Plus. 137 (5): 555. arXiv:2205.07908. Bibcode:2022EPJP..137..555S. doi:10.1140/epjp/s13360-022-02773-w. ISSN 2190-5444. S2CID 248652864.

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